1. The Vertex of a Parabola Finding the Maximum or Minimum

2. The Graph of a Parabola Parabolas all have the same shape but they can be oriented in different directions, depending on the equation. This is the general equation of parabolas that open up or down.

3. Parabola Opening Upwards If a is positive, the graph opens upwards. 3 is positive – graph opens upwards

4. Parabola Opening Downwards If a is negative, the graph opens downwards. 3 is negative – graph opens downwards

5. The Vertex of a Parabola The vertex of a parabola is the low point if it opens upward. Vertex This is called a minimum.

6. The Vertex of a Parabola The vertex of a parabola is the high point if it opens downward. Vertex This is called a maximum.

7. Axis of Symmetry of a Parabola The axis of symmetry of a parabola passes through the vertex.

8. Axis of Symmetry of a Parabola The axis of symmetry of a parabola passes through the vertex. If we folded the parabola across the axis of symmetry, the left side and the right side would match up. We can say that the graph is symmetric with respect to the line.

9. Axis of Symmetry Formula The formula for the axis of symmetry of a parabola that opens up or down is: The axis of symmetry is a vertical line. We’re expecting an equation in the form x = a number.

10. Axis of Symmetry of a Parabola Let’s look at an example: Axis of symmetry

11. Vertex of a Parabola The vertex is on the axis of symmetry. To find the y-coordinate of the vertex, substitute the value you found for x into the equation of the parabola. Vertex: (-1, -12)

12. Remember a is positivea is negative graph opens upgraph opens down vertex is a minimumvertex is a maximum